Bessel functions Jv(x) and Yv(x) of real order and real argument

1979 ◽  
Vol 18 (1) ◽  
pp. 133-142 ◽  
Author(s):  
J.B. Campbell
Keyword(s):  
Bessel Functions ◽  
Real Argument

Conical functions with one or both parameters large

1991 ◽  
Vol 119 (3-4) ◽  
pp. 311-327 ◽  
Author(s):  
T. M. Dunster
Keyword(s):  
Positive Constant ◽  
Asymptotic Expansions ◽  
Bessel Functions ◽  
Legendre Functions ◽  
Elementary Functions ◽  
The Real ◽  
Complex Argument ◽  
Arbitrary Positive Constant ◽  
Real Argument ◽  
Uniform Asymptotic Expansions

SynopsisUniform asymptotic expansions are derived for conical functions, Legendre functions of order µ and degree −½ + iτ, where µ and τ are non-negative real parameters. As τ → ∞, expansions are furnished for the conical functions which involve Bessel functions of order µ. These expansions are uniformly valid for 0 ≦ µ ≦ Aτ (A an arbitrary positive constant), and are also uniformly valid for Re (z) ≧ 0 in the complex argument case, and 0 ≦ z < ∞ in the real argument case. The case µ → ∞ is also considered, and expansions are furnished which are uniformly valid in the same z regions for 0 ≦ τ ≧ Bµ (B an arbitrary positive constant); in the cases where Re(z) ≧ 0 and 1 ≦ z < ∞, the expansions involve Bessel functions of purely imaginary order iτ, and in the case where 0 ≦ z < 1 the expansions involve elementary functions.

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